Greetings matey!
The first Cutlass weapon quest is for level 4 cutlass (Given at level 15 cutlass) and is called the "Fine Cutlass".
The 2nd quest for level 5 cutlass (given at level 20 cutlass) is the "Pirate Blade".
I am unaware of any "Grand Cutlass" quest unless they changed something. Not familiar with a "Grand Doll" either, sorry.
The quests/tasks for the Fine Cutlass, and the Pirate Blade can be viewed on the wiki.
http://www.disneyonlineworlds.com/index.php/Potco
Best of luck to ye!